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Subject: Anyone caculated the EVs for the various perk options? rss

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Cthulhu Dreams
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I was looking at the Mindthief's perk options, and it seems that the expected value of all the first options is roughly the same, but the EV is going to change dramatically with the SECOND perk selection.

Has anyone done any simulations about this? Is there an easily configurable tool so you could run the simulation?
 
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Troy Laurin
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CthulhuDreams wrote:
... and it seems that the expected value of all the first options is roughly the same ...

I'm not sure how you come to this conclusion, at all.
Spoiler (click to reveal)
Assuming an attack value of 2, the starting modifier deck is a bell curve with a mean of 0 and standard deviation of 1.170. Picking the "Remove two -1 cards" perk changes that to 0.11 +/-1.182 (EV is 0.11+/-0.012), whereas "Remove four +0 cards" instead goes to 0 +/- 1.31 (EV is 0+/-0.14)

I have no idea how to calculate the EV of a stun or pull modifier; negative conditions are situationally great, but only if they are a condition that is appropriate for the moment or you can play one of the two attacks that do extra damage to an enemy with conditions. Or some other player can take advantage. But the stun modifier while usually great, is wasted if you kill the enemy with that attack.

The EV of ignoring negative scenario effects should be calculable for a particular scenario (it's trivially 0 in a scenario with no negative effects), but what is the EV of a curse card? Consider that you will draw it only once rather than re-shuffling it into the deck, so the EV will be proportional to the number of modifiers you expect to draw in a scenario.

Notwithstanding, all of these bell curve calculations are indicative but wrong, since each draw from the deck has a memory of every draw that wasn't the 2x or 0x card. It might be a fun project for a CS or finance major to mock all of this up in a monte-carlo simulation, but without a way to quantify the value of non-numeric effects the results are going to be incomplete... and without simulating the full game, including interaction between other players, the results are going to be misleading.

Still might be fun, and a way to get practical experience with monte carlo principles.
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Luke Turner
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You can easily check the numeric value of a perk by listing out the draw deck in a spreadsheet (like Excel). Use +4 and -4 for the x2 and the null or whatever value you feel is sensible. Add an average equation on the bottom and then you can get a good idea. You then can directly affect your 'deck' and remove, add, or change values.

Off hand I can tell you that numerically getting rid of the -1's is the most bang for your buck even for the Second perk (raising the overall value of your deck by 2 and then dividing by 2 less cards), but that's not taking into account the effects you could generate with the elemental and status perks.

Honestly it's kind of overkill to min/max this way, but it can be fun I suppose. I wouldn't take out the 4 '0' cards until you've purged the lower value cards, as all that will do is make your deck more swingy without changing the average much (none if it's your first perk).


Edit: Since MrTroy went there and included memory in his answer, I'll say that my method above does not of course include such concepts. You could go nuts and thoroughly map this out as he suggested, but doing what I wrote above will give you a rough estimate of avg with the full deck.
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Cthulhu Dreams
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MrTroy wrote:
CthulhuDreams wrote:
... and it seems that the expected value of all the first options is roughly the same ...

I'm not sure how you come to this conclusion, at all.
Spoiler (click to reveal)
Assuming an attack value of 2, the starting modifier deck is a bell curve with a mean of 0 and standard deviation of 1.170. Picking the "Remove two -1 cards" perk changes that to 0.11 +/-1.182 (EV is 0.11+/-0.012), whereas "Remove four +0 cards" instead goes to 0 +/- 1.31 (EV is 0+/-0.14)

I have no idea how to calculate the EV of a stun or pull modifier; negative conditions are situationally great, but only if they are a condition that is appropriate for the moment or you can play one of the two attacks that do extra damage to an enemy with conditions. Or some other player can take advantage. But the stun modifier while usually great, is wasted if you kill the enemy with that attack.

The EV of ignoring negative scenario effects should be calculable for a particular scenario (it's trivially 0 in a scenario with no negative effects), but what is the EV of a curse card? Consider that you will draw it only once rather than re-shuffling it into the deck, so the EV will be proportional to the number of modifiers you expect to draw in a scenario.

Notwithstanding, all of these bell curve calculations are indicative but wrong, since each draw from the deck has a memory of every draw that wasn't the 2x or 0x card. It might be a fun project for a CS or finance major to mock all of this up in a monte-carlo simulation, but without a way to quantify the value of non-numeric effects the results are going to be incomplete... and without simulating the full game, including interaction between other players, the results are going to be misleading.

Still might be fun, and a way to get practical experience with monte carlo principles.


Yeah, sorry I should be clear. Remove 4 +0 cards is obviously the worst, the others though are similar in value:

remove two -1 cards
replace two +1 cards with two +2 cards
replace one -2 card with +0 card
add two +1 draw again cards

Remove two -1 cards seems best, mean value of a draw rises to +0.111 vs 0.1 for the other ones but it's quite simplistic.

I think any build that doesn't wear armor is going to start with remove 2x -1's twice, (any build that wears armor will start with the ignore negative item effects perk, particularly the Brute's ignore negative item effects perk which is super strong) but once you've done that it's very interesting.
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Luke Turner
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CthulhuDreams wrote:


Yeah, sorry I should be clear. Remove 4 +0 cards is obviously the worst, the others though are similar in value:


Remove +0 is only the worst for the first few perks. It gains a lot of value once you have other cards in your deck you want to get to though. Once you have some 'rolling' cards and only one -1 and the null as 'bad' cards clearing out 4 meh cards looks a lot more promising.
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Cthulhu Dreams
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sakoguru wrote:
CthulhuDreams wrote:


Yeah, sorry I should be clear. Remove 4 +0 cards is obviously the worst, the others though are similar in value:


Remove +0 is only the worst for the first few perks. It gains a lot of value once you have other cards in your deck you want to get to though. Once you have some 'rolling' cards and only one -1 and the null as 'bad' cards clearing out 4 meh cards looks a lot more promising.


Yeah, so this is the question - when does that happen? It's not clear it's true for the first 3 perks so far, and maybe even longer. The hardest part to caculate in excel is the +1 damage rolling modifier cards though as their interaction with 2x and Null is complex.

Remove two -1 cards
Remove two -1 cards
either of -2 -> 0 or two +1 become +2

Looks better than removing four +0. Mean attack card value for removing two -1 twice then removing four +0: 0.333333333 StDEv 2.015094554 vs 0.375 StdEv 1.62788206 for my above scenarios


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Cthulhu Dreams
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Based on some preliminary testing, I'm starting to think pure card quality is the way forward, depending on the values you assign to the roll over modifiers. It seems a good leveling plan for the mind thief is

1) Remove two -1 cards
2) Remove two -1 cards
3) Either replace -2 card with a +0 card or replace two+1 with two +2 cards (second option has more variance)
4) Whichever one you didn't select the first time
5) Remove 4 * +0 cards

Unless you want cold elemental powers the rolling modifiers seem a lot better from this point forwards.

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Luke Turner
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I'd get rid of all the negatives you can before even considering the remove 4 +0 cards. Other than that though the Rolling Stun and Rolling Disarm + Rolling Muddle perks are really appealing.
 
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Troy Laurin
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CthulhuDreams wrote:
Remove two -1 cards seems best, mean value of a draw rises to +0.111 vs 0.1 for the other ones but it's quite simplistic.

I'm okay starting with simplistic :-) I'd disagree that removing two -1s seems best for at least the first choice.

Consider the probabilities that you draw a good card, a neutral card or a negative card:

Base: 35% good (ave +1.28), 35% bad (ave -1.28)
Remove x2 -1s: 39% good (ave +1.28), 28% bad (ave -1.4)
Remove x4 +0s: 44% good (ave +1.28), 44% bad (ave -1.28)
Replace x2 +1 with +2: 35% good (ave +1.57), 35% bad (ave -1.28)
Replace x1 -2 with +0: 35% good (ave +1.28), 30% bad (ave -1.17)
Add x1 +2: 38% good (ave +1.38), 33% bad (-1.28)

So things are less likely to go bad if you remove the -1s compared to the -2, but when they do go bad the results will tend to be worse. The odds are nearly as good if you switch the -2, but you also decrease the average downside when a bad card is drawn.

Personally (I'm playing a mindthief), I'd replace the -2 before removing -1s to reduce variance and let me plan better. +2 ice is probably compelling for the second choice because our party has a spellweaver.

sakoguru wrote:
I'd get rid of all the negatives you can before even considering the remove 4 +0 cards. Other than that though the Rolling Stun and Rolling Disarm + Rolling Muddle perks are really appealing.

I definitely like the idea of condition modifiers, but without a streamlined deck I suspect they just aren't going to come out at the right time.
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Noel Szczepanski
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CthulhuDreams wrote:
I was looking at the Mindthief's perk options, and it seems that the expected value of all the first options is roughly the same, but the EV is going to change dramatically with the SECOND perk selection.

Has anyone done any simulations about this? Is there an easily configurable tool so you could run the simulation?


Yes. I have every combination calculated for every class. I'll get around to posting them. Here is a snippet in the mean time. I did these calculations using the variant rule (which is mathematically superior). I'll do another set using the normal rules.

A: Remove two -1s
B: Remove four 0s
C: Replace two +1 with two +2
D: Replace one -2 with one 0
E: Add one +2 and frost
F: Add two +1 and draw another
G: Add three Pull 1 and draw another
H: Add three Muddle and draw another
I: Add two Immobilize and draw another
J: Add one Stun and draw another
K: Add on Disarm and one Muddle and draw another

# of PERKS CODE AVG SD
1 D 0.1000 0.8307
1 A 0.1111 0.9362
2 AD 0.2222 0.7857
2 AA 0.2500 0.9014
3 AAD 0.3750 0.6960
4 AADG 0.3750 0.6960
4 AABC 0.5000 1.1902


The spreadsheet I created is dynamic enough to enter in negative items from cards, scenario effects, and targets with armor. I'm currently working on making it more user-friendly and less.... huge.
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This is an interesting read.

Though, just bear in mind that any overkill damage is wasted. I'll just go to an illustrative example of a perk:

* replace one +100 card by +200

I don't know all the numbers, but I guess that this one is really, really useless. Any +100 will suffice to remove the target. Adding another +100 won't matter, even though your average modifier draw greatly increases. Removing a -1 will be significantly better.

Going back down to realistic numbers, I guess that switching a card from -1 to 0 is usually better than going from 0 to +1. And what perk is most efficient will depend on both the enemies you face and the action cards you intend to use.

So while these calculations are interesting and show a part of the effect, I'm afraid that there is no way to determine the impact of a perk by simple math. shake

If someone were to build a computer model of dungeon, hand cards and modifier deck and run a couple million Monte-Carlo-Markov-Chains, though …
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Luke Turner
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PiHalbe wrote:

So while these calculations are interesting and show a part of the effect, I'm afraid that there is no way to determine the impact of a perk by simple math. shake


For sure. The simple math here is minor in usefulness, but fun none the less.

Ultimately for me though I plan to get rid of the negative cards any chance I get, simply because nothing is worse during the game than winding up for a good hit and drawing a -1 or -2 (or worse, the null that can't be removed anyway). A +0 still feels like you're doing what you expected, and +1 or +2 values are just icing on the cake.
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Felix Scholz
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PiHalbe wrote:
[...]Going back down to realistic numbers, I guess that switching a card from -1 to 0 is usually better than going from 0 to +1. [...] …


That depends on your playstyle. If you are attacking a monster with two hit points with you basic Attack 2, swapping a -1 for a 0 is of course better than swapping a 0 for -1 in this case.
However if you have removed almost all of your negative modifier you might count on + damage from modifier cards when planning your turn.
If you attack a monster with 5 hitpoints for example you might then choose to go for the Attack 4 card instead of attack 6 (and save that one for later) because you know you have a good chance you will kill it anyway.

What I'm trying to say is: Most of the perks are situational to some degree. Swapping/adding/removing +/- modifiers probably less so than rolling modifiers with effects but there are always situations where the other choice would have been better. But I really like how some perks get better once you have picked up others. The depths in these decisions is something you don't find in your usual dungeon crawler and are part of the reason I expect that I will love this game (once I get it *grumble*).
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Troy Laurin
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PiHalbe wrote:
So while these calculations are interesting and show a part of the effect, I'm afraid that there is no way to determine the impact of a perk by simple math. shake

MrTroy wrote:
Notwithstanding, all of these bell curve calculations are indicative but wrong, since each draw from the deck has a memory of every draw that wasn't the 2x or 0x card. It might be a fun project for a CS or finance major to mock all of this up in a monte-carlo simulation, but without a way to quantify the value of non-numeric effects the results are going to be incomplete... and without simulating the full game, including interaction between other players, the results are going to be misleading.

laugh

Quote:
If someone were to build a computer model of dungeon, hand cards and modifier deck and run a couple million Monte-Carlo-Markov-Chains, though …

If I didn't have a full time job, a toddler at home and a 10kg box of boardgame to try to organise, I'd probably have fun trying to do up a monte-carlo of at least the numeric attack modifiers. I'm curious now just how much the memory modelling would deviate from the memoryless modelling of mean/stdev that's going on.

P0isson wrote:
I did these calculations using the variant rule (which is mathematically superior). I'll do another set using the normal rules.

I'm curious why you say it's mathematically superior. It certainly changes the results - switching the 2x and 0x cards to be +0 causes the A perk to decrease the SD compared to the base deck, but it actually increases the SD compared to the base deck if playing them as 2x and 0x, as long as you're attacking with a rating >= 2. If you're planning on using high-value attacks with the base rules then the only perks that reduce the "swinginess" of the results are D and ... possibly F.

You didn't include any F results in your snippet so I can't be sure, but if you're modelling it as just a +1 card then the results will be wrong, as the card value actually ranges from -1 to ((x+1)x2)

For the record, I don't plan on modelling my perk choices in my campaign It does make for an interesting discussion though.
 
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Marc Alexandre
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For me, the most important is to reduce the chance to get the worst. What's the worst? The Null card, then the -2, then the -1. The 0 are neutral, they're ignored by my logic.

Removing the four 0s is greatly increasing the chance of the Null card. So it will be one of the latest perks for me. The most important is to remove the -2. Then it's a combination between removing the -1, and adding more cards to try to keep the chances to draw the Null card as low as possible. The Null card is really the worst that can happen. Even if you try to get advantage as many time as you can, it can still screw you at the worst possible time, so it's really important to manage this, more than increasing the global value of the deck (at least for me).

Of course, if you play the "low luck" variant, removing the negative cards is the priority.
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tibbles von tibbleton
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I was just about to head to bed, so probably shouldn't start overthinking this now, but my gut impression is this doesn't give enough weight to the null. That's negating all, not just 2 damage, and one would assume that a fair bit of the 2x bonus damage will be wasted, so it is worth less than full double. Thus the deck is tilted negative due solely to the null. It makes me wonder that if removing cards (the +0s, at least) is undesirable in order to reduce chances of drawing the null and increase consistency.

Edit: Dangit, ninja'd. But at least I'm not the only one thinking this. Consistency and avoiding the null is more important to planning than upping deck strength.

I like that above idea of swapping the -2 first. After that, I think I'd need to be more awake to consider removing -1s vs adding the +2. It'd be the balance between adding thickness vs the fact that as noted, a portion of the +2 will go to waste every so often while the -1 applies much of the time, so it's not an equal EV change of 2*-1 vs +2.
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Cthulhu Dreams
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You can fairly easily do a simplistic but valuable model a dungeon particularly for the mindthief. Take the two player scenario balance formula that Isaac published for the scenario design competition, divide the monster count by 2 to get what a 'typical' arrangement of HP sacks would look like, then assume the mindthief opens by playing the +2 attack augment then plays generic attack 2 cards until his hand expires, short rests and repeats.

It is hugely simplistic but gives you a working model that is close enough to expose the relative merits of taking cards out.
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Marc Alexandre
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It's good from a theory point. But if you got the Null card at the only moment you must not get it, because you've trim down your deck to 12 cards, the fact that overall you're making more damages is not important at this moment. I know that you should never be in this position, and in the long run you should be better because of this. But I'm an unlucky guy. 1 bad card out of 12 would be drawn really often on my bad days. I mean, I lost my first two battles against Ancient in my last game of Eclipse with one, then two dreadnoughts because of unlucky throw, even though I hade 75% and then 90+% chance of winning those fights. When I'm having bad luck, it doesn't stop.
 
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sakoguru wrote:
CthulhuDreams wrote:


Yeah, sorry I should be clear. Remove 4 +0 cards is obviously the worst, the others though are similar in value:


Remove +0 is only the worst for the first few perks. It gains a lot of value once you have other cards in your deck you want to get to though. Once you have some 'rolling' cards and only one -1 and the null as 'bad' cards clearing out 4 meh cards looks a lot more promising.


The problem is there's no way to remove the null and making your deck smaller increases your chance of drawing it. If you had some way to always make sure you had advantage I guess it wouldn't be an issue.
 
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I at least partially agree with Marc. Raising average damage is important, but you might overkill enemies. Reducing chances of total failure is another very important aspect, since the ability to plan your damage as exact as possible gives you more control over your actions. Cutting down your deck size too much has the potential to hinder you.
 
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Jimmy Brazelton
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I feel like all of these analyses and most of the comments here are assuming the goal is to maximize the damage that you produce. But since the OP is specifically playing a Mindthief (which happens to be my class as well), I think that damage is really a secondary consideration in this deck, at least in a full party of 4 people.

We're playing with a Scoundrel, Cragheart, Tinkerer, and me, the Mindthief. While I can certainly do some serious damage when I want, I've noticed that if I focus my role more on status effects, I am of more value to the team. So while it is really tempting to take out those -1 cards ASAP, I've instead opted to get all of the rolling status modifier cards in my deck first before I worry about damage. I'm also adding Curse enhancements to my cards when I can (need to increase prosperity!). With this type of build, nearly every attack I make will stun, immobilize, disarm, and/or curse an enemy.

Maybe a pure damage-focused build is actually more effective, but since other classes are focused on that, I've found that being a tiny ball of fur that jumps behind enemy lines and takes away half of the enemies' turns on an early initiative at the start of a scenario, and then turns invisible, is a highly entertaining way to play.
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tibbles von tibbleton
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That is a goood point. If your goal is more about the status effects, then avoiding the null at the cost of a thick deck is less important. Instead you probably want the smallest deck possible so you can keep reshuffling and redrawing the effects. In that case, pruning 4 0s is quite good.
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tibbles wrote:
That is a goood point. If your goal is more about the status effects, then avoiding the null at the cost of a thick deck is less important. Instead you probably want the smallest deck possible so you can keep reshuffling and redrawing the effects. In that case, pruning 4 0s is quite good.


Yep. I will probably do this before taking out any of the negative cards for this exact reason. My only concern is that in my "final" deck, I may end up OVER affecting my targets. After all, if an enemy is disarmed, who cares if it's also muddled?
 
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One thing I'd note is that characters can donate for blessings, which changes the value of thinning out your deck.

Also, just as effective monster health sets a practical cap on the net value of an attack, shield and/or low attack cards can compress the lower value cards into the same net value as well. If I play my Cragheart 1 damage (without consuming Earth) 7 hex AoE Muddle on enemies with Shield 1, cards of zero, null, -1 or -2 all do the same damage.
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MrTroy wrote:

I'm curious why you say it's mathematically superior. It certainly changes the results - switching the 2x and 0x cards to be +0 causes the A perk to decrease the SD compared to the base deck, but it actually increases the SD compared to the base deck if playing them as 2x and 0x, as long as you're attacking with a rating >= 2. If you're planning on using high-value attacks with the base rules then the only perks that reduce the "swinginess" of the results are D and ... possibly F.


The variance decreases with the variant; the tails are cut off.

It is superior because the normal bless/curse rules are essentially +100% and -100% effects. However, the +100% side is capped by monster health so at its absolute best - the attack doesn't overkill the monster - it actually does the full 100%. In most cases however, you get overkill, and usually quite a bit. But even say, only 10% of the time you get overkill then the results is +90% (on average) and -100% which is a net -5% effect to your deck. Meanwhile the alternate is a net 0% change.

Furthermore, reduced variability is much better, and arguably more important than increased average damage. As stated before overkill is a waste but just as wasteful is leaving a monster alive with 1 hp left. If you reduce the variability of your deck you can be more certain of the result of your attack.

MrTroy wrote:

You didn't include any F results in your snippet so I can't be sure, but if you're modelling it as just a +1 card then the results will be wrong, as the card value actually ranges from -1 to ((x+1)x2)


The modeling of the +1 w/redraw and the pierce 3 perks is more challenging but I did correctly model them. I should have thought to go that far in the snippet to show this. To calculate the +1redaw and pierce you need to do some combinations nCr for the probability of each and then multiply by the increasing probability of drawing a card that ends all draws (including bless and curse).
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